Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 4 : pp. 374–386
Abstract
In this paper, using spectral decimation, we prove that the "hot spots" conjecture holds on a class of homogeneous hierarchical gaskets introduced by Hambly, i.e., every eigenfunction of the second-smallest eigenvalue of the Neumann Laplacian (introduced by Kigami) attains its maximum and minimum on the boundary.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2017-0070
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 4 : pp. 374–386
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Neumann Laplacian ”hot spots” conjecture homogeneous hierarchical gasket spectral decimation analysis on fractals.